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10: Pauli Spin Matrices

  • Page ID
    56862
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    We can represent the eigenstates for angular momentum of a spin-1/2 particle along each of the three spatial axes with column vectors:

    \[\begin{aligned}
    &|+z\rangle=\left[\begin{array}{l} 1 \\ 0 \end{array}\right] \quad|+y\rangle=\left[\begin{array}{l} 1 / \sqrt{2} \\ i / \sqrt{2}
    \end{array}\right] \quad|+x\rangle=\left[\begin{array}{l} 1 / \sqrt{2} \\
    1 / \sqrt{2} \end{array}\right] \\ &|-z\rangle=\left[\begin{array}{l} 0 \\ 1 \end{array}\right] \quad|-y\rangle=\left[\begin{array}{l}
    i / \sqrt{2} \\ 1 / \sqrt{2}
    \end{array}\right] \quad|-x\rangle=\left[\begin{array}{r} 1 / \sqrt{2} \\ -1 / \sqrt{2} \end{array}\right]
    \end{aligned}\tag{10.1} \nonumber\]

    Similarly, we can use matrices to represent the various spin operators.


    This page titled 10: Pauli Spin Matrices is shared under a CC BY-NC-SA 4.0 license and was authored, remixed, and/or curated by Pieter Kok via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.

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